Unexpected spontaneous symmetry breaking and diverse ferroicity in two-dimensional mono-metal phosphorus chalcogenides.

Mono-metal phosphorus trichalcogenides (MPX3) have attracted intensive interest due to their intriguing magnetic properties and potential applications. Generally, single-layer two-dimensional (2D) MPX3 are believed to be centrosymmetric. However, we discovered that unexpected spontaneous symmetry breaking may occur in some 2D MPX3, i.e., vertical P-P dimers move out of the plane and become tilted, leading to the structural stability being enhanced, the inversion symmetry being simultaneously broken, and ferroelectricity or ferroelasticity emerging. By systematically investigating the family (176) of 2D MPX3, we found that 34 members undergo such symmetry breaking during geometric optimization, in which ten are identified to be dynamically stable. We show that the mismatch between the triangular sublattice of P-P dimers and the hexagonal sublattice of M atoms and the variable accommodation of P lone-pair electrons in different valence states of M atoms play dominant roles in the inversion symmetry breaking and the emergence of ferroicity. We obtained a ferroic atlas of the whole 2D MPX3 family, which also includes many stable antiferromagnetic and non-ferroic members that have never been reported. Our work not only presents ferroelectricity in the 2D MPX3 family but also reveals how diverse ferroicity emerges with various spontaneous symmetry breakings, which will be helpful for further exploration of 2D ferroic materials.

Two-Dimensional Intercalating Multiferroics with Strong Magnetoelectric Coupling.

Intrinsic two-dimensional (2D) multiferroics that couple ferromagnetism and ferroelectricity are rare. Here, we present an approach to achieve 2D multiferroics using powerful intercalation technology. In this approach, metal atoms such as Cu or Ag atoms are intercalated in bilayer CrI3 to form Cu(CrI3)4 or Ag(CrI3)4. The intercalant leads to the inversion symmetry breaking and produces a large out-of-plane electric polarization with a low transition barrier and a small reversal electric field, exhibiting excellent 2D ferroelectric properties. In addition, due to charge transfer between the intercalated atoms and bilayer CrI3, the interlayer coupling transits from antiferromagnetic to ferromagnetic, and the intralayer ferromagnetic coupling is also enhanced. Furthermore, the built-in electric polarization causes a distinct surface magnetization difference, generating a strong magnetoelectric coupling with a coefficient larger than that of Fe, Co, and Ni thin films. Our work paves a practical path for 2D multiferroics, which may have crucial applications in spintronics.

Ferroelectric and Room-Temperature Ferromagnetic Semiconductors in the 2D MIMIIGe2X6 Family: First-Principles and Machine Learning Investigations.

Inspired by experimentally discovering ferromagnetism and ferroelectricity in two-dimensional (2D) CrGeTe3 and CuInP2S6 with similar geometric structures, respectively, we systematically investigated ferroic properties in a large family of 2D MIMIIGe2X6 (MI and MII = metal elements, X = S/Se/Te) by combining high-throughput first-principles calculations and the machine learning method. We identified 12 stable 2D multiferroics containing simultaneously ferromagnetic (FM) and ferroelectric (FE) properties and 35 2D ferromagnets without FE polarization. Particularly, the predicted FM Curie temperatures (TC) of eight 2D FM+FE semiconductors are close to or above room temperature. The ferroelectricity originates from the spontaneous geometric symmetry breaking induced by the unexpected shift of Ge-Ge atomic pairs and the emergence of Ge lone pair electrons, which also strengthens the p-d orbital hybridization between X atoms and metal atoms, leading to enhanced super-super-exchange interactions and raising the FM TC. Our findings not only enrich the family of 2D ferroic materials and present room-temperature FM semiconductors but also disclose the mechanism of the emerging ferroelectricity and enhanced ferromagnetism, which sheds light on the realization of high temperature multiferroics as well as FM semiconductors.

High-efficient ab initio Bayesian active learning method and applications in prediction of two-dimensional functional materials.

Beyond the conventional trial-and-error method, machine learning offers a great opportunity to accelerate the discovery of functional materials, but still often suffers from difficulties such as limited materials data and the unbalanced distribution of target properties. Here, we propose the ab initio Bayesian active learning method that combines active learning and high-throughput ab initio calculations to accelerate the prediction of desired functional materials with ultrahigh efficiency and accuracy. We apply it as an instance to a large family (3119) of two-dimensional hexagonal binary compounds with unbalanced materials properties, and accurately screen out the materials with maximal electric polarization and proper photovoltaic band gaps, respectively, whereas the computational costs are significantly reduced by only calculating a few tenths of the possible candidates in comparison with a random search. This approach shows the enormous advantages for the cases with unbalanced distribution of target properties. It can be readily applied to seek a broad range of advanced materials.

Voting Data-Driven Regression Learning for Accelerating Discovery of Advanced Functional Materials and Applications to Two-Dimensional Ferroelectric Materials.

Regression machine learning is widely applied to predict various materials. However, insufficient materials data usually leads to poor performance. Here, we develop a new voting data-driven method that could generally improve the performance of the regression learning model for accurately predicting properties of materials. We apply it to investigate a large family (2135) of two-dimensional hexagonal binary compounds focusing on ferroelectric properties and find that the performance of the model for electric polarization is indeed greatly improved, where 38 stable ferroelectrics with out-of-plane polarization including 31 metals and 7 semiconductors are screened out. By unsupervised learning, actionable information such as how the number and orbital radius of valence electrons, ionic polarizability, and electronegativity of constituent atoms affect polarization was extracted. Our voting data-driven method not only reduces the size of materials data for constructing a reliable learning model but also enables one to make precise predictions for targeted functional materials.

Large family of two-dimensional ferroelectric metals discovered via machine learning.

Ferroelectricity and metallicity are usually believed not to coexist because conducting electrons would screen out static internal electric fields. In 1965, Anderson and Blount proposed the concept of "ferroelectric metal", however, it is only until recently that very rare ferroelectric metals were reported. Here, by combining high-throughput ab initio calculations and data-driven machine learning method with new electronic orbital based descriptors, we systematically investigated a large family (2964) of two-dimensional (2D) bimetal phosphates, and discovered 60 stable ferroelectrics with out-of-plane polarization, including 16 ferroelectric metals and 44 ferroelectric semiconductors that contain seven multiferroics. The ferroelectricity origins from spontaneous symmetry breaking induced by the opposite displacements of bimetal atoms, and the full-d-orbital coinage metal elements cause larger displacements and polarization than other elements. For 2D ferroelectric metals, the odd electrons per unit cell without spin polarization may lead to a half-filled energy band around Fermi level and is responsible for the metallicity. It is revealed that the conducting electrons mainly move on a single-side surface of the 2D layer, while both the ionic and electric contributions to polarization come from the other side and are vertical to the above layer, thereby causing the coexistence of metallicity and ferroelectricity. Van der Waals heterostructures based on ferroelectric metals may enable the change of Schottky barrier height or the Schottky-Ohmic contact type and induce a dramatic change of their vertical transport properties. Our work greatly expands the family of 2D ferroelectric metals and will spur further exploration of 2D ferroelectric metals.